Hi all, Sorry - me again. I think i have a bit of a gap in my understanding. So i do understand that the graph on page 659 on the CMP clearly has a trend, and so we would say its not stationary. However, what i dont understand is the equation X_n=0.1n+0.5X_(n-1)+e_n Is this not an AR(1) process - and following this, the root 1/0.5= 2 is greater than 1 in magnitude, so i would say it was stationary? i assume its the 0.1n that is causing the problems, could someone clear this up please? Thanks so much in advance
Hi Molly As you point out, the problem is the 0.1n. If we just had: X_n = 0.5 * X_(n-1) + e_n then this is a stationary AR(1) process. However, adding 0.1*n to this means we no longer have an AR process. This type of term does not appear in the definition of an AR model. For a process to be an AR process, it must have the structure: X_n = mu + a_1 * (X_(n-1) - mu) + a_2 * (X_(n-2) - mu) + ... + a_p * (X_(n-p) - mu) + e_n or: X_n = constant + a_1 * X_(n-1) + a_2 * X_(n-2) + ... + a_p * X_(n-p) + e_n These two expressions are just rearrangements of each other. In particular, the inclusion of the 0.1*n means that the process is not stationary as, for example, the mean will change over time. Hope this helps! Andy
